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The '''Dirac equation''', published by [[Paul Dirac]] in 1928, is the relativistic wave equation for spin-&frac12; particles such as the [[Electron]].

==The standard account==

Dirac sought a wave equation first order in time, as [[Quantum Mechanics]] requires, and also first order in space, as [[Special Relativity]] symmetry suggests. Meeting both conditions forced him to introduce four anticommuting matrices and a four-component wave function &mdash; the bispinor. Three results followed with no further assumptions:

* '''Spin.''' Electron spin of one-half, previously inserted by hand, emerges from the structure of the equation, together with the gyromagnetic ratio ''g'' = 2 (the small deviation from 2 is a quantum-electrodynamic effect, calculated and measured to more than ten digits).
* '''Fine structure.''' The equation reproduces the fine structure of the [[Hydrogen Atom]] spectrum correctly.
* '''Antimatter.''' The equation has negative-energy solutions. Dirac's interpretation &mdash; a filled "sea" of negative-energy states whose holes appear as positive particles of opposite charge &mdash; predicted the positron, which Carl Anderson observed in cosmic rays in 1932.

In modern quantum field theory the negative-energy sea is dropped: the Dirac field is quantised, and the antiparticle appears as a distinct excitation. The equation remains the foundation of relativistic quantum mechanics and of the electron sector of the Standard Model.

==On this wiki==

The Dirac equation is invoked constantly in the quantum-alternative literature catalogued here, generally by authors seeking a deterministic or classical reading of what the bispinor describes.

* [[Robert A Close]]'s [[A Dirac Equation]] (2008) argues that the equation is fundamentally deterministic &mdash; an evolution equation for angular momentum density &mdash; and shows that a classical second-order wave equation for angular momentum density in an elastic solid is equivalent to a bispinor equation. He argues the conventional parity operator is derived incorrectly, and that wave interference in this reading produces both the Lorentz force and the [[Pauli Exclusion Principle]].
* [[Don L Hotson]]'s [[Dirac's Equation and the Sea of Negative Energy, Part 1]] and its sequel argue that the negative-energy sea was discarded prematurely and that much of modern physics has been built around the omission.
* [[Peter Rowlands]] approaches the equation algebraically in [[Breaking the Dirac Code]], deriving particle structure from a nilpotent formulation.
* [[Milo M Wolff]] and others in [[:Category:Quantum Theory]] pursue wave-structure-of-matter readings of electron spin.
* [[Genuine Subharmonic Equations to Replace Those of Schrödinger and Dirac]] proposes replacements outright.

Common to most of these is not a claim that the equation's predictions are wrong &mdash; they are among the best confirmed in physics &mdash; but the claim that its probabilistic interpretation is optional, and that a physical wave in a medium underlies it.

==See also==

* [[Paul Dirac]]
* [[Electron]]
* [[Spin]]
* [[Pauli Exclusion Principle]]
* [[Quantum Mechanics]]
* [[Special Relativity]]

[[Category:Quantum Theory]]
[[Category:Particle Physics]]
[[Category:Theory & Models]]